Henri & Renaud Lifchitz's PRP Top records

What is a PRP ?

A PRP is a probable prime number, a number that nobody knows how to prove or disprove its primality.
Here are some criterions that can be used to recognize these numbers :

- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3. N should pass the strong test in base b.
- or more (if someone has got an idea) !!!

Submit your PRPs

See the Top discoverers
See the Latest PRPs
Search by form


1-250	251-500	501-750	751-1000	1001-1250	1251-1500	1501-1750	1751-2000
2001-2250	2251-2500	2501-2750	2751-3000	3001-3250	3251-3500	3501-3750	3751-4000
4001-4250	4251-4500	4501-4750	4751-5000	5001-5250	5251-5500	5501-5750	5751-6000
6001-6250	6251-6500	6501-6750	6751-7000	7001-7250	7251-7500	7501-7750	7751-8000
8001-8250	8251-8500	8501-8750	8751-9000	9001-9250	9251-9500	9501-9750	9751-10000

Rank	Probable prime	Digits (> 30000)	Who ?	When ?
8001	2^204323-2221	61508	Yves Minet	08/2013
8003	2^204317-195	61506	Lelio R Paula	08/2011
8002	3^128910-86	61506	Lelio R Paula	04/2013
8004	2^204318+74539	61506	Enzo Doria	04/2016
8005	(2^204334-3)/1141333	61505	Lelio R Paula	03/2012
8006	2^204297-1036093	61500	Paul Bourdelais	11/2012
8007	3^128880+58	61492	Lelio R Paula	04/2013
8008	2^204216-111677	61476	Enzo Doria	05/2014
8009	(F(73524)^5-F(73523)^5)/F(73522)	61462	Wayne Halsdorf	03/2012
8010	2^204129+204129	61449	Henri Lifchitz	04/2002
8011	3^128787+2^(128787-1)	61448	Robert Price	05/2016
8012	11^58999-78	61442	Lelio R Paula	05/2013
8013	2^204083-111967	61436	Enzo Doria	05/2014
8014	(45^37159+1)/46	61431	Robert Price	11/2013
8015	677^21702+21702^677	61430	Norbert Schneider	06/2016
8016	14837^13810+13810^14837	61429	Hans Havermann	02/2017
8017	(7*2^204043+1)/39	61423	Lelio R Paula	03/2012
8018	11^58976-1740	61418	Enzo Doria	11/2012
8019	2^204016-16085	61415	Enzo Doria	04/2013
8020	V(379967)	61393	Serge Batalov	03/2015
8021	43777!3-3^43777	61392	Robert Price	08/2015
8022	7^72642+88	61390	Lelio R Paula	04/2013
8023	3^128656+32	61385	Lelio R Paula	04/2013
8024	2^203916-17493	61385	Enzo Doria	05/2013
8025	6^78880+23	61381	Lelio R Paula	04/2013
8026	(388*10^61374-1)/9	61376	Robert Price	11/2017
8027	2^203877-111799	61374	Enzo Doria	05/2014
8028	2^203867-1615	61371	Lelio R Paula	10/2011
8029	4*10^61367+19	61368	Robert Price	04/2016
8030	(19*2^203854+1)/42319	61363	Lelio R Paula	08/2012
8031	L(293659)/76528122719	61361	Serge Batalov	07/2017
8032	2^203825-15805	61358	Enzo Doria	04/2013
8033	2^203816-15825	61355	Enzo Doria	04/2013
8034	5*10^61348+59	61349	Robert Price	09/2016
8035	21^46395-2	61345	Lelio R Paula	08/2013
8036	(809*29^41946-165)/28	61344	Curtis Bright	05/2015
8037	7*6^78826+5	61340	Lelio R Paula	09/2014
8038	(3^128558+7)/83773166429696	61324	Lelio R Paula	04/2012
8039	2^203706-111	61322	Lelio R Paula	08/2011
8040	17567^3094+3094^17567	61318	Hans Havermann	02/2017
8041	2^203689-31	61317	Thomas Masser	10/2005
8042	(11*2^203678-1)/53689	61310	Lelio R Paula	01/2014
8043	2^203642+39	61303	Lelio R Paula	08/2011
8044	floor(Pi*10^61382)%(10^61303)	61303	Serge Batalov	07/2012
8045	11^58849-6040	61285	Enzo Doria	02/2013
8046	43694!3-3	61264	Robert Price	10/2014
8047	58(10^(320420)-1)/111-1	61260	Robert Price	10/2014
8048	2^203490+12909	61257	Lelio R Paula	10/2011
8049	(16*10^61251-31)/3	61252	Robert Price	03/2016
8050	20^47077-5703	61249	Enzo Doria	03/2013
8051	2^203434-113081	61240	Enzo Doria	07/2014
8053	5^87606+4	61234	Wojciech Florek	11/2005
8052	2^203412-167	61234	Lelio R Paula	08/2011
8054	2^203402+1089	61231	Lelio R Paula	10/2011
8055	(8*10^61230+67)/3	61231	Robert Price	01/2017
8056	(2^203408+lucasV(1,2,203408)+1)/(2*32993)	61228	Mike Oakes	11/2016
8057	1265^19732+19732^1265	61211	Serge Batalov	05/2014
8058	2^203330+145	61209	Lelio R Paula	08/2011
8059	6^78647-137	61200	Lelio R Paula	04/2013
8060	85^31718+84	61198	Norbert Schneider	10/2015
8061	11^58763-270	61196	Enzo Doria	07/2012
8062	2^203285-112321	61195	Enzo Doria	06/2014
8063	2^203253-995143	61186	Paul Bourdelais	11/2012
8064	15319^9862+9862^15319	61184	Hans Havermann	07/2016
8065	7^72395-44	61181	Lelio R Paula	04/2013
8066	(49*10^61167-67)/9	61168	Robert Price	08/2017
8067	5*2^203176-7	61163	Lelio R Paula	04/2014
8068	(26*10^61156-413)/9	61157	Robert Price	10/2017
8070	7^72358+54	61150	Lelio R Paula	04/2013
8069	2^203133-111775	61150	Enzo Doria	05/2014
8071	(lucasV(1,2,406356)+2)/(3^251119315836979671743)	61145	Mike Oakes	01/2017
8072	2^203112-18009	61143	Enzo Doria	05/2013
8073	43607!3+729	61129	Robert Price	09/2014
8074	2^203065-114853	61129	Enzo Doria	05/2015
8075	3^128111+196	61125	Lelio R Paula	04/2013
8076	128^29007+29007^128	61124	Serge Batalov	05/2014
8077	4*10^61119+49	61120	Robert Price	08/2017
8078	22355*2^203009-3	61117	Donovan Johnson	03/2004
8079	2^203018+33	61115	Lelio R Paula	08/2011
8080	2^203017-1615	61115	Lelio R Paula	10/2011
8081	16697^4570+4570^16697	61110	Hans Havermann	12/2016
8082	2^202998-17241	61109	Enzo Doria	05/2013
8083	20^46964+93	61102	Lelio R Paula	06/2013
8084	(55*10^61097-1)/9	61098	Ray Chandler	02/2012
8085	20^46960-5463	61097	Enzo Doria	03/2013
8086	(11*10^61095+49)/3	61096	Robert Price	05/2016
8087	2^202934-5955	61090	Lelio R Paula	10/2011
8088	19^47772-68	61089	Lelio R Paula	05/2013
8089	2^202877-499423	61073	Paul Bourdelais	03/2013
8090	2^202763-17125	61038	Enzo Doria	05/2013
8091	(23*2^202756+1)/9	61037	Lelio R Paula	03/2012
8092	14788^13355+13355^14788	61011	Hans Havermann	12/2016
8093	16069^6258+6258^16069	61005	Hans Havermann	12/2016
8094	5^87276-14336	61004	Enzo Doria	02/2013
8095	50^35899-49^35899	60992	Robert Price	12/2012
8096	2^202599-3049	60989	Yves Minet	10/2014
8097	2^202535-111571	60970	Enzo Doria	05/2014
8098	(13*10^60966+107)/3	60967	Robert Price	11/2017
8100	10^60959+57	60960	Patrick De Geest	12/2008
8099	6*10^60959-91	60960	Robert Price	11/2017
8102	10^60959-60959	60959	Henri Lifchitz	08/2002
8101	10^60959-29177	60959	Patrick De Geest	08/2008
8103	5^87206+4^(87206+1)	60955	Robert Price	07/2016
8104	2^202476-15909	60952	Enzo Doria	04/2013
8105	2^202472-17513	60951	Enzo Doria	05/2013
8106	14858^12651+12651^14858	60950	Hans Havermann	12/2016
8107	2^202389-58695	60926	Lelio R Paula	09/2011
8108	3^127597-34	60880	Lelio R Paula	04/2013
8109	15088^10831+10831^15088	60876	Hans Havermann	12/2016
8110	2^202198-113261	60868	Enzo Doria	07/2014
8111	2^202182+135	60863	Lelio R Paula	08/2011
8112	2^202176+85	60862	Lelio R Paula	08/2011
8113	5183^16384+5182^16384	60860	Henri Lifchitz	01/2007
8114	(31*2^202163+1)/3	60859	Lelio R Paula	03/2012
8115	14708^13707+13707^14708	60847	Hans Havermann	12/2016
8116	2^202112+202112^2-1	60842	Robert Price	04/2014
8117	(13*2^202142-1)/405984274257	60841	Lelio R Paula	01/2014
8118	64743*10^60832+(6^78175-11)/5	60837	Gilbert Mozzo	05/2012
8119	(19*2^202098-1)/6795	60836	Lelio R Paula	01/2014
8120	(6^78175-11)/5	60832	Paul Bourdelais	11/2011
8121	2^202063+1605	60828	Lelio R Paula	09/2011
8122	2^202058+859	60826	Lelio R Paula	09/2011
8123	1576^19021+19021^1576	60821	Serge Batalov	05/2014
8124	(2^202009+3)/6005	60807	Lelio R Paula	03/2012
8125	10^60776+3	60777	Robert Price	01/2011
8126	10^60776-14819	60776	Patrick De Geest	12/2012
8127	55*10^60772+7	60774	Robert Price	10/2017
8128	(6883*2^201869-1)/35	60771	Lelio R Paula	04/2015
8129	(27*2^201841-1)/43	60760	Lelio R Paula	01/2014
8130	2^201822-177	60755	Lelio R Paula	08/2011
8131	(13*10^60744+17)/3	60745	Robert Price	06/2015
8132	(31*2^201754-1)/99	60734	Lelio R Paula	01/2014
8133	(26*10^60717-71)/9	60718	Robert Price	03/2015
8134	37^38712-2	60709	Lelio R Paula	08/2013
8135	2^201657-112003	60705	Enzo Doria	05/2014
8136	(10^60703+3^60703)/13	60702	Robert Price	01/2013
8137	2^201622-112817	60695	Enzo Doria	06/2014
8138	2^201620-17177	60694	Enzo Doria	05/2013
8139	(2^201615-3)*6-7	60693	Gilbert Mozzo	05/2016
8140	2^201609-49789	60691	Henri Lifchitz	03/2005
8141	2^201582-19061	60683	Enzo Doria	05/2013
8142	43316!3+27	60679	Robert Price	09/2014
8143	(509203*2^201564-1)/5067	60679	Lelio R Paula	04/2015
8144	2^201560+105	60676	Lelio R Paula	08/2011
8145	(27*2^201584-1)/646755486457	60673	Lelio R Paula	01/2014
8146	2^201545-18021	60672	Enzo Doria	05/2013
8147	2^201543+11715	60671	Lelio R Paula	09/2011
8148	2^201512-111755	60662	Enzo Doria	05/2014
8149	p(13013)#/2+64	60662	Robert Price	03/2017
8150	11^58248+16	60660	Lelio R Paula	05/2013
8151	2^201496-27	60657	Lelio R Paula	08/2011
8152	5*10^60655+57	60656	Robert Price	11/2017
8153	(7*10^60643+197)/3	60644	Robert Price	07/2017
8154	2^201426-16097	60636	Enzo Doria	04/2013
8155	(17*10^60631-11)/3	60632	Robert Price	07/2015
8156	6^77916-77	60631	Lelio R Paula	04/2013
8157	(27*2^201410-1)/491	60630	Lelio R Paula	01/2014
8158	5^86727+98	60620	Lelio R Paula	04/2013
8159	17^49266-26	60620	Lelio R Paula	05/2013
8160	20^46589-33	60614	Lelio R Paula	05/2013
8161	6^77889+65	60610	Lelio R Paula	04/2013
8162	139901#+148387	60595	Nicolas PALAU	09/2016
8163	2^201285-111723	60593	Enzo Doria	05/2014
8164	46199*2^201268+129647	60593	Paul Vanderveen	11/2016
8166	3^126991-100	60591	Lelio R Paula	04/2013
8165	2^201278-111623	60591	Enzo Doria	05/2014
8167	5^86682-16004	60589	Enzo Doria	05/2014
8168	(865*10^60583-1)/9	60585	Robert Price	11/2017
8169	(58*10^60579+221)/9	60580	Robert Price	02/2017
8170	9*2^201231-5	60578	Lelio R Paula	04/2014
8171	4*10^60572-89	60573	Robert Price	08/2017
8172	(78557*2^201207+1)/13067	60571	Lelio R Paula	06/2014
8173	2^201186-66945	60564	Lelio R Paula	09/2011
8174	2^201186-94395	60564	Lelio R Paula	09/2011
8175	65^33403+32	60557	Lelio R Paula	01/2016
8176	103^30079+102	60545	Norbert Schneider	10/2016
8177	(1000159^10091+1)/1000160	60541	Faysal YAtim	08/2008
8178	2^201098-17717	60537	Enzo Doria	05/2013
8179	(3^126881+8)/4829	60534	Lelio R Paula	03/2012
8180	2^201074+75049	60530	Enzo Doria	04/2016
8181	11^58111-1290	60517	Enzo Doria	11/2012
8182	(509203*2^201012-1)/9	60516	Lelio R Paula	04/2015
8183	2^200911+5711	60481	Lelio R Paula	10/2011
8184	(2^200912-3)/23	60480	Lelio R Paula	03/2012
8185	18^48179-17^48179	60478	Jean-Louis Charton	12/2010
8187	38^38281-37^38281	60476	Robert Price	09/2012
8186	4*7^71560-3	60476	Lelio R Paula	09/2014
8188	(10^(230232+1)+1510^30232-1)/3	60465	Robert Price	04/2016
8189	lucasV(1,2,401712)+2	60464	Mike Oakes	01/2017
8190	2^200833-18493	60457	Enzo Doria	05/2013
8191	20^46465-5043	60453	Enzo Doria	03/2013
8192	2^200810-18257	60450	Enzo Doria	05/2013
8193	((2)^(2*100400-1)+(2)^(100400-1)+1)+26672	60447	Faysal YAtim	04/2018
8194	5^86466-14336	60438	Enzo Doria	02/2013
8195	Phi(145558,10)/103928413/161714939/14779231531/36075385837/242411419853	60432	Maksym Voznyy	10/2011
8196	(29*2^200703-1)/231	60417	Lelio R Paula	01/2014
8197	2^200682-1016831	60412	Paul Bourdelais	11/2012
8198	2^200617-17881	60392	Enzo Doria	05/2013
8199	(25^43201+1)/26	60391	Robert Price	06/2013
8201	2^200609-133	60390	Lelio R Paula	08/2011
8200	2^200608-12837	60390	Enzo Doria	10/2012
8202	2^200607-17121	60389	Enzo Doria	05/2013
8203	11^57975-1620	60375	Enzo Doria	11/2012
8204	(9913*2^200538-1)/3801	60369	Lelio R Paula	04/2015
8205	5^86342+64	60351	Lelio R Paula	04/2013
8206	(14*10^60346-23)/9	60347	Robert Price	04/2015
8207	2^200457-8295	60344	Lelio R Paula	09/2011
8208	6^77546+113	60343	Lelio R Paula	04/2013
8210	37^38461-36^38461	60315	Robert Price	06/2012
8209	2^200361-17593	60315	Enzo Doria	05/2013
8211	10103^15059-106	60304	Enzo Doria	07/2012
8212	2^200301-17401	60297	Enzo Doria	05/2013
8213	(37*10^60290+71)/9	60291	Robert Price	04/2015
8214	2^200266-94395	60287	Lelio R Paula	09/2011
8215	2^200261-111613	60285	Enzo Doria	05/2014
8216	46^36238-45	60256	Norbert Schneider	07/2014
8217	13^54091+94	60255	Lelio R Paula	05/2013
8218	311^24171-154	60253	Enzo Doria	07/2012
8219	2^200120-81089	60243	Paul Bourdelais	01/2012
8220	3^126262+8680	60243	Lelio R Paula	04/2013
8221	43031!3-59049	60239	Robert Price	12/2015
8222	2^200100-111269	60237	Enzo Doria	05/2014
8223	(29*2^200069-1)/5373	60225	Lelio R Paula	01/2014
8224	20^46283-1923	60216	Enzo Doria	03/2013
8225	2^200011-112075	60210	Enzo Doria	05/2014
8226	2^200002+74539	60207	Enzo Doria	04/2016
8227	(386027912^200026-1)/(5778492645749*3427009)	60203	Jens K. Andersen	09/2007
8228	(28*10^60180+149)/3	60181	Robert Price	10/2017
8229	2^199872+93	60168	Donovan Johnson	06/2008
8230	6^77321+77	60168	Lelio R Paula	04/2013
8231	(86*10^60165-77)/9	60166	Robert Price	05/2016
8232	(2^199868+78557)/23373	60162	Lelio R Paula	05/2012
8233	7^71180+82	60155	Lelio R Paula	04/2013
8235	2^199814-112295	60151	Enzo Doria	06/2014
8234	(51^35227-1)/50	60151	Paul Bourdelais	08/2017
8236	42964!3-81	60135	Robert Price	09/2014
8237	2^199709-51	60119	Lelio R Paula	05/2011
8238	2^199700-111623	60116	Enzo Doria	05/2014
8239	(15185*2^199681-1)/159	60112	Lelio R Paula	04/2015
8240	2^199672+2533	60108	Henri Lifchitz	09/2004
8241	20^46198-11	60105	Lelio R Paula	04/2013
8242	2^199657+93257	60103	Yves Minet	03/2010
8243	3^125967-110	60102	Lelio R Paula	10/2012
8244	2^199654-18813	60102	Enzo Doria	05/2013
8245	(29*10^60100+19)/3	60101	Robert Price	01/2017
8246	2^199615-2*199615+1	60091	Robert Price	04/2018
8247	129^28468+28468^129	60085	Serge Batalov	05/2014
8248	2^199572-15873	60078	Enzo Doria	04/2013
8249	9*2^199559+7	60075	Lelio R Paula	03/2014
8250	2^199527-111919	60064	Enzo Doria	05/2014

Find by discoverer :

PRP Records

Probable Primes Top 10000

(224926 PRPs in the top)